What's causing this mesh error?
Your body mesh seems to have a lot of duplicate faces.  You can see this even by moving around the model in the viewport...those weird marks are the geometry fighting:



Another way to see is if you select a face on the torso and choose "Select->Select Similar->Material" and you'll get most, but not all, of the faces.  

I would suggest selecting ALL of the vertices of the body model, then choosing Mesh->Vertices->Remove Doubles.  That will remove the extra geometry.  

Unfortunately then you will have patches of the torso that are a different material (so they'll be purple) but you can select one of those, again do "Select->Select Similar->Material" and set them to the same material as the rest of the Torso.  Or vice versa, depending on what you want. 

You might have to re-rig after removing the doubled geometry, but it will solve your rogue pieces sticking out.